Question: What is $\frac{1}{3}$ of $\frac{1}{4}$ of $\frac{1}{5}$ of 60?
We multiply the fractions by $60$ to get $\frac13\times\frac14\times\frac15\times60=\frac{60}{3\times4\times5}=\frac{60}{60}=\boxed{1}$.